Mathematical Quotes

Are mathematical ideas invented or discovered? This question has been repeatedly posed by philosophers through the ages and will probably be with us forever.

The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another.

A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.

The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it.

Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.

A time will however come (as I believe) when physiology will invade and destroy mathematical physics, as the latter has destroyed geometry.

There can be no question, however, that prolonged commitment to mathematical exercises in economics can be damaging. It leads to the atrophy of judgement and intuition. . .

The mathematical sciences wield their particular language made of digits and signs, no less subtle than any other.

The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical] notation.

Data-driven statistics has the danger of isolating statistics from the rest of the scientific and mathematical communities by not allowing valuable cross-pollination of ideas from other fields.

The mathematical expectation of the speculator is zero.

I'm obviously attuned to pick up mathematics whenever I can see it. But in Mozart there is a lot of conscious use of mathematical symbolism and numbers in order to try and give messages.

The circumstances of human society are too complicated to be submitted to the rigor of mathematical calculation.

It's like a mathematical law, Grace.

We will never fully explain the world by appealing to something outside it that must simply be accepted on faith, be it an unexplained God or an unexplained set of mathematical laws.

Theoretical physicists accept the need for mathematical beauty as an act of faith... For example, the main reason why the theory of relativity is so universally accepted is its mathematical beauty.

A book on the new physics, if not purely descriptive of experimental work, must essentially be mathematical.

Mathematical physics is in the first place physics and it could not exist without experimental investigations.

I've always had a more spatial mind, mathematical, than literal.

If there is something very slightly wrong in our definition of the theories, then the full mathematical rigor may convert these errors into ridiculous conclusions.

Strange! I don't understand how it is that we can write mathematical expressions and calculate what the thing is going to do without being able to picture it.

Mathematical Mark all mathematical heads, which be only and wholly bent to those sciences, how solitary they be themselves, how unfit to live with others, and how unapt to serve in the world.

There has to be a mathematical explanation for how bad that tie is.

Here at Wisconsin we didn't get an undergraduate course in mathematical logic until the '60s.

Why does the universe go to all the bother of existing?

The universe is governed by science. But science tells us that we can't solve the equations, directly in the abstract.

The explorer is the person who is lost.

It is clear that economics, if it is to be a science at all, must be a mathematical science.

Sometimes a line of mathematical research extending through decades can be thought of as one long conversation in which many mathematicians take part. This is fortunately true at present.

The Mandelbrot set is the most complex mathematical object known to mankind.

Neither concepts nor mathematical formulae can explain the infinite.

The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.

As for explaining mathematical phenomena it opens the question: explaining to whom? humans?, other computers?

Music is a secret and unconscious mathematical problem of the soul.

Mathematical high culture collides with pop culture and all hell breaks loose! Harris takes us on a wild ride--never a dull moment!

My reasons are the same as for any mathematical conjecture: (1) It is a legitimate mathematical possibility, and (2) I do not know.

Maybe because I can't even put together an IKEA desk, I've never been tempted to think of my own poems as built objects - but I do sometimes imagine them as mathematical constructs.

This ambiguity is another example of a growing problem with mathematical notation: There aren't enough squiggles to go around.

MacPherson told me that my theorem can be viewed as blah blah blah Grothendieck blah blah blah, which makes it much more respectable.

Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.

For me, rhythm is a type of divine mathematics in a way. No matter where you're from, we can all understand the mathematics of rhythm. I try to apply this mathematical thinking to my playing.

Most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician.

Chess will always be in the doldrums as a spectator sport while a draw is given equal mathematical value as a decisive result.

The mathematical fraternity is a little like a self-perpetuating priesthood. The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom to admit to the priesthood.

The next grand extensions of mathematical physics will, in all likelihood, be furnished by quaternions.

Criticized for using formal mathematical manipulations, without understanding how they worked: Should I refuse a good dinner simply because I do not understand the process of digestion?

It seems to me that all the evidence points to Apollonius as the founder of Greek mathematical astronomy.

Gauss replied, when asked how soon he expected to reach certain mathematical conclusions, that he had them long ago, all he was worrying about was how to reach them!

I was reminded of the Sydney Harris cartoon that said 'adding two numbers that have not been added before does not constitute a mathematical breakthrough'.

Cyberspace is the human transition into a mathematical super space where we as a collectivity become optionally a single point of view.